Details

sample239.0ms

Algorithm

intervals

Results

9.0ms	36×	body	2560	valid
8.0ms	184×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	18×	body	640	valid
3.0ms	8×	body	160	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.7b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune151.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Merged error: 5.7b

Counts

93 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.4b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
49.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune237.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	219	10	229

Merged error: 5.6b

Counts

229 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.1b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.8b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
28.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
53.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
42.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune315.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	500	3	503
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	504	9	513

Merged error: 5.6b

Counts

513 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 169

Calls

4 calls:

13.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	618	2276
1	2684	2086
2	5001	1951

prune96.0ms

Filtered

81 candidates to 181 candidates (-123.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	182	8	190

Merged error: 5.6b

Counts

190 → 8

regimes374.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.8b

bsearch96.0ms

Steps

Iters	Range	Point
7	7.012417207579252e+108	1.3633655355432952e+110	2.821264388342136e+109
10	-7.55890950842511e-252	-1.434145681223809e-265	-2.6427022137303496e-260
9	-8.123118303304505e+80	-8.66777673642249e+74	-3.453036615513107e+80

Iters

Range

Point

7.012417207579252e+108

1.3633655355432952e+110

2.821264388342136e+109

-7.55890950842511e-252

-1.434145681223809e-265

-2.6427022137303496e-260

-8.123118303304505e+80

-8.66777673642249e+74

-3.453036615513107e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	42	22
2	42	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

273.0ms	1105×	body	2560	valid
249.0ms	5833×	body	80	valid
166.0ms	855×	body	1280	valid
117.0ms	2890×	body	80	nan
72.0ms	470×	body	640	valid
33.0ms	113×	body	5120	valid
27.0ms	233×	body	320	valid
10.0ms	129×	body	160	valid

Details

sample239.0ms

simplify13.0ms

prune5.0ms

localize11.0ms

rewrite30.0ms

series71.0ms

simplify142.0ms

prune151.0ms

localize11.0ms

rewrite50.0ms

series120.0ms

simplify109.0ms

prune237.0ms

localize11.0ms

rewrite93.0ms

series122.0ms

simplify107.0ms

prune315.0ms

localize15.0ms

rewrite36.0ms

series67.0ms

simplify73.0ms

prune96.0ms

regimes374.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample1.4s

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